Abstract
This paper investigates the robust passivity problem for neural networks with uncertain system parameters and a time-varying delay. Based on Lyapunov stability theory, ensuring the negative definiteness for the derivatives of the developed Lyapunov-Krasovskii functional (LKF) is necessary in order to derive a passivity criterion. A negative condition on the cubic polynomial over a certain interval is developed in this paper, which introduces some slack matrices to obtain an advanced negative condition. Taking advantage of this condition, an augmented LKF with more system state and delay function information, including several augmented vectors and a single-integral-based term, is constructed. Then some improved passivity criteria for delayed neural networks are derived on top of the proposed LKF and the negative condition. Finally, the effectiveness and superiority of the obtained passivity criteria are validated on two numerical examples.
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Yaqi Li received her B.Sc. and M.Sc. degrees from Hunan University of Technology in 2016 and 2020, respectively. She is an engineer at National Innovation Center of Advanced Rail Transit Equipment, Zhuzhou, China. Her research interests include time-delay systems, robust control, and machine learning.
Yun Chen received his M.Sc. degree in control theory and control engineering from Hunan University of Technology, Zhuzhou, China, in 2020. He is currently pursuing a Ph.D. degree with State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China. His current research interests include security and privacy in cyber-physical systems, networked control systems, and time-delay systems.
Shuangcheng Sun is the director of Institute of New Energy System, National Innovation Center of Advanced Rail Transit Equipment, Zhuzhou, China. He received his S.M., M.E., and Ph.D. degrees from Harbin Institute of Technology, in 2013, 2015, and 2018, respectively. His main fields of interest and expertise include automatic control, inverse heat transfer, radiative heat transfer, thermal energy storage, and optimization algorithms.
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Li, Y., Chen, Y. & Sun, S. Improved Robust Passivity Criteria for Delayed Neural Networks. Int. J. Control Autom. Syst. 22, 927–935 (2024). https://doi.org/10.1007/s12555-022-0878-x
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DOI: https://doi.org/10.1007/s12555-022-0878-x